reserve G,G1,G2 for _Graph;
reserve W,W1,W2 for Walk of G;
reserve e,x,y,z for set;
reserve v for Vertex of G;
reserve n,m for Element of NAT;

theorem
  for W being Path of G, e, v being object st e Joins W.last(),v,G & not v
  in W.vertices() & (W is trivial or W is open) holds W.addEdge(e) is Path-like
  by Lm68;
